Scheduling a batching machine

Brucker, Peter; Gladky, Andrei; Hoogeveen, Han; Kovalyov, Mikhail Y.; Potts, Chris N.; Tautenhahn, Thomas; Velde, S.L. van de

doi:10.1002/(sici)1099-1425(199806)1:1<31::aid-jos4>3.0.co;2-r

Cited by 346 publications

(136 citation statements)

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“…The case of B = +∞ can be solved in polynomial time if all jobs arrive at time zero, by a dynamic programming algorithm of Brucker et al [2]. In this section we show that it becomes NP-complete when jobs arrive at different times.…”

Section: Np-completeness Proofmentioning

confidence: 99%

“…This is a contradiction Let J (k) denote the set of jobs which has length P k , let X (k) j be the set of jobs with length P k and release date > r j , and let X (k) j,i denote the set of jobs with length P k and release date r , r j < r ≤ r i . Let OPT(t k , X (1) , X (2) , . .…”

Section: Job Set With a Constant Number Of Processing Timesmentioning

confidence: 99%

“…Brucker et al give a thorough discussion of the scheduling problem of the batch machine under various constraints and objective functions [2]. For the objective of minimizing the weighted total completion time, their discussion was restricted for the case that job arrival times are all zero.…”

mentioning

confidence: 99%

“…For the objective of minimizing the weighted total completion time, their discussion was restricted for the case that job arrival times are all zero. In particular, Brucker et al point out that the case with unequal arrival times is much more difficult, even when B = +∞ [2].…”

mentioning

confidence: 99%

“…More precisely, when B = +∞ (or equivalently B ≥ n for a system of n jobs), the problem 1|r j , B| w j C j is NP-complete. Previous NP-hardness results for this problem either restrict B to be bounded and/or have other constraints on the jobs, such as sizes [11] and deadlines [2].…”

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confidence: 99%

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Minimizing Mean Completion Time in a Batch Processing System

Deng

Hu²,

Zhang³

et al. 2003

Algorithmica

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We consider batch processing jobs to minimize the mean completion time. A batch processing machine can handle up to B jobs simultaneously. Each job is represented by an arrival time and a processing time. Jobs processed in a batch have the same completion time, i.e., their common starting time plus the processing time of their longest job. For batch processing, non-preemptive scheduling is usually required and we discuss this case. The batch processing problem reduces to the ordinary uniprocessor system scheduling problem if B = 1. We focus on the other extreme case B = +∞. Even for this seemingly simple extreme case, we are able to show that the problem is NP-hard for the weighted version. In addition, we establish a polynomial time algorithm for a special case when there are only a constant number of job processing times. Finally, we give a polynomial time approximation scheme for the general case.

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Section: Np-completeness Proofmentioning

confidence: 99%

Section: Job Set With a Constant Number Of Processing Timesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Minimizing Mean Completion Time in a Batch Processing System

Deng

Hu²,

Zhang³

et al. 2003

Algorithmica

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Scheduling batches with simultaneous job processing for two-machine shop problems

2001

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We consider the problem of scheduling independent jobs on two machines in an open shop, a job shop and a flow shop environment. Both machines are batching machines, which means that several operations can be combined into a batch and processed simultaneously on a machine. The batch processing time is the maximum processing time of operations in the batch, and all operations in a batch complete at the same time. Such a situation may occur, for instance, during the final testing stage of circuit board manufacturing, where burn‐in operations are performed in ovens. We consider cases in which there is no restriction on the size of a batch on a machine, and in which a machine can process only a bounded number of operations in one batch. For most of the possible combinations of restrictions, we establish the complexity status of the problem. Copyright © 2001 John Wiley & Sons, Ltd.

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